Implementation aspects of sequential Gaussian simulation on irregular points

Abstract

The increasing use of unstructured grids for reservoir modeling motivates the development of geostatistical techniques to populate them with properties such as facies proportions, porosity and permeability. Unstructured grids are often populated by upscaling high-resolution regular grid models, but the size of the regular grid becomes unreasonably large to ensure that there is sufficient resolution for small unstructured grid elements. The properties could be modeled directly on the unstructured grid, which leads to an irregular configuration of points in the three-dimensional reservoir volume. Current implementations of Gaussian simulation for geostatistics are for regular grids. This paper addresses important implementation details involved in adapting sequential Gaussian simulation to populate irregular point configurations including general storage and computation issues, generating random paths for improved long range variogram reproduction, and search strategies including the superblock search and the k-dimensional tree. An efficient algorithm for computing the variogram of very large irregular point sets is developed for model checking.